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2 years ago

There is a large number of cubes in a bag.

Mathematics

1 answer:

Alla [95]2 years ago

7 0

Marked(10)/total = 3/20 (from sample)

total/10 = 20/3 (inverting the above proportion)

total = 10•20/3 = 200/3 ≈ 67

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______ x ________ = 16

Arlecino [84]

1) 4 times 4 = 16
2) 2 times 2 times 9 = 36
3) 4 times 2 times 9 = 72
4) x + y + z = n
(any solution that is true)

6 0

2 years ago

Rosa is putting cube-shaped tissue boxes into a shipping crate. each tissue box has a side length of 4 inches. The volume of V o

Elena L [17]

Answer:

V = 64 and V = 2,048

Step-by-step explanation:

The volume of a cube is found using V = s*s*s. Substitute s = 4.

The volume is V = 4*4*4 = 64.

The volume of the crate is 32 * 64 = 2,048.

3 0

2 years ago

One positive number is 14 less than another positive number. If the reciprocal of the smaller number is added to five times the

Kipish [7]

Let's call the two numbers $s$ and $l$ .

Given these variables, we can say: $s = l - 14$ , based on the first sentence in the problem.

Also, remember that the reciprocal of a number is simply 1 divided by the number. Thus, we can say that:

$\dfrac{1}{s} + 5\Big( \dfrac{1}{l} \Big) = \dfrac{1}{4}$

To solve, we can simply substitute $l -14$ in for $s$ in the second equation and solve.

$\dfrac{1}{l - 14} + \dfrac{5}{l} = \dfrac{1}{4}$

Set up

$\dfrac{l}{l(l - 14)} + \dfrac{5(l - 14)}{l(l - 14)} = \dfrac{1}{4}$

Get terms on the left side to a common denominator for easier addition

$\dfrac{l + 5l - 70}{l(l - 14)} = \dfrac{1}{4}$

Simplify

$4(6l - 70) = l(l - 14)$

Cross multiplication ( $\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc$ )

$24l - 280 = l^2 - 14l$

Simplify

$l^2 - 38l + 280 = 0$

Subtract $24l - 280$ from both sides of the equation

$(l - 10)(l - 28) = 0$

Factor left side of the equation

$l = 10, 28$

Zero Product Property

Now, notice that we have found two solutions, but the problem is only asking for one. This <em>likely </em>means that one of our solutions is extraneous. Let's take a look. Remember that the smaller positive number is equal to 14 less than the larger number. However,

$s = 10 - 14 = -4$ ,